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Dynamic structure factor of the three-dimensional Ising model with purely relaxational dynamics
Pasquale Calabrese1, Victor Martín-Mayor, Andrea Pelissetto
1Scuola Normale Superiore and INFN, Sezione di Pisa, I-56100 Pisa, Italy. Pasquale.Calabrese@df.unipi.it
Summary
We calculated the dynamic structure factor for the 3D Ising model using epsilon expansion and Monte Carlo simulations. Results show the mean-field Gaussian form accurately approximates the dynamic structure factor.
Area of Science:
- Statistical physics
- Condensed matter physics
Background:
- The three-dimensional Ising model is a fundamental model in statistical mechanics.
- Understanding its dynamic properties, particularly the dynamic structure factor, is crucial for characterizing phase transitions and critical phenomena.
Purpose of the Study:
- To compute the dynamic structure factor for the 3D Ising model with relaxational dynamics (Model A).
- To compare theoretical calculations with simulation results and assess the validity of approximations.
Main Methods:
- Perturbative calculation using epsilon expansion at two loops (high-temperature phase) and one loop (temperature-magnetic field plane).
- Monte Carlo simulation in the high-temperature phase.
Main Results:
- The dynamic structure factor is well approximated by the mean-field Gaussian form.
- Deviations from the Gaussian form are minimal (a few percent) within the investigated range of momentum (kξ ≤ 5) and frequency (ωτ ≤ 10).
Conclusions:
- The mean-field Gaussian approximation provides a robust description of the dynamic structure factor for the 3D Ising model under relaxational dynamics.
- Theoretical and simulation results are in good agreement, validating the employed methods.